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Popular >

derivative of 2^{sin(x})

Solution

\frac{d}{d x} (2^{s i n (x)})

Solution

ln (2) \cdot 2^{s i n (x)} cos (x)

Solution steps

\frac{d}{d x} (2^{s i n (x)})

Apply exponent rule:

a^{b} = e^{b l n (a)}

2^{s i n (x)} = e^{s i n (x) l n (2)}

= \frac{d}{d x} (e^{s i n (x) l n (2)})

Apply the chain rule:

e^{s i n (x) l n (2)} \frac{d}{d x} (sin (x) ln (2))

= e^{s i n (x) l n (2)} \frac{d}{d x} (sin (x) ln (2))

\frac{d}{d x} (sin (x) ln (2)) = ln (2) cos (x)

= e^{s i n (x) l n (2)} ln (2) cos (x)

e^{s i n (x) l n (2)} = 2^{s i n (x)}

= ln (2) \cdot 2^{s i n (x)} cos (x)

Graph

Popular Examples

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\int_{0}^{4} \frac{ln ( x )}{x} d x

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sin^{2} (x)

d/(dt)(3cos(t))

\frac{d}{d t} (3 cos (t))

limit as x approaches 0 of 3ln(x)

x \to 0 lim (3 ln (x))

integral of sin^3(t)cos^8(t)

\int sin^{3} (t) cos^{8} (t) d t

Frequently Asked Questions (FAQ)

What is the derivative of 2^{sin(x}) ?
The derivative of 2^{sin(x}) is ln(2)*2^{sin(x)}cos(x)
What is the first derivative of 2^{sin(x}) ?
The first derivative of 2^{sin(x}) is ln(2)*2^{sin(x)}cos(x)